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It is known that for finite Rossby numbers geostrophically balanced flows develop specific ageostrophic instabilities. We undertake a detailed study of the Rossby-Kelvin (RK) instability, previously studied by Sakai (J. Fluid Mech...
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It is known that for finite Rossby numbers geostrophically balanced flows develop specific ageostrophic instabilities. We undertake a detailed study of the Rossby-Kelvin (RK) instability, previously studied by Sakai (J. Fluid Mech., vol. 202, 1989, pp. 149-176) in a two-layer rotating shallow-water model. First, we benchmark our method by reproducing the linear stability results obtained by Sakai (1989) and extend them to more general configurations. Second, in order to determine the relevance of RK instability in more realistic flows, simulations of the evolution of a front in a continuously stratified fluid are carried out. They confirm the presence of RK instability with characteristics comparable to those found in the two-layer case. Finally, these simulations are used to study the nonlinear saturation of the RK modes. It is shown that saturation is achieved through the development of small-scale instabilities along the front which modify the mean flow so as to stabilize the RK mode. Remarkably, the developing instability leads to conversion of kinetic energy of the basic flow to potential energy, contrary to classical baroclinic instability.
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Being motivated by the recent experiments on instabilities of the two-layer flowsin the rotating annulus with super-rotating top, we perform a full stability analysisfor such system in the shallow-water approximation. We use the c...
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Being motivated by the recent experiments on instabilities of the two-layer flowsin the rotating annulus with super-rotating top, we perform a full stability analysisfor such system in the shallow-water approximation. We use the collocation methodwhich is benchmarked by comparison with analytically solvable one-layer shallow-water equations linearized about a state of cyclogeostrophic equilibrium. We describedifferent kinds of instabilities of the cyclogeostrophically balanced state of solid-body rotation of each layer (baroclinic, Rossby—Kelvin (RK) and Kelvin—Helmholtz(KH) instabilities), and give the corresponding growth rates and the structure of theunstable modes. We obtain the full stability diagram in the space of parameters ofthe problem and demonstrate the existence of crossover regions where baroclinic andRK, and RK and KH instabilities, respectively, compete having similar growth rates.
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Four major sources of inertia-gravity waves are known in the Earth atmosphere: upper-tropospheric jet-streams, lower-tropospheric fronts, convection and topography. The Andes Cordillera region is an area where all of these major s...
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Four major sources of inertia-gravity waves are known in the Earth atmosphere: upper-tropospheric jet-streams, lower-tropospheric fronts, convection and topography. The Andes Cordillera region is an area where all of these major sources are potentially present. By combining ECMWF and NCEP-NCAR reanalysis, satellite and ra-diosoundings data and mesoscale WRF simulations in the Andes Cordillera region, we were able to identify the cases where, respectively, the jet-stream source, the convective source and the topography source are predominantly in action. We retrieve emitted wave parameters for each case, compare them, and analyse possible emission mechanisms. The WRF mesoscale model shows very good performance in reproducing the inertia-gravity waves identified in the data analysis, and assessing their likely sources.
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This paper is focused on the spontaneous transient adjustment of a buoyant lens of water with uniform density, initially at rest in the vicinity of the equator. For parameters typical of the western Pacific warm pool, the adjustme...
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This paper is focused on the spontaneous transient adjustment of a buoyant lens of water with uniform density, initially at rest in the vicinity of the equator. For parameters typical of the western Pacific warm pool, the adjustment is shown to generate finite-amplitude wave motions with period ～8 days, which are not covered by the standard theory of linear equatorial waves. This mechanism may be at the origin of inertial motions at the early stages of ENSO events in the western Pacific Ocean. The lens adjustment is studied within the 1(1/2)-iayer reduced-gravity approximation on the equatorial β plane, using the high-resolution finite-volume numerical methods that are specially designed to handle outcropping isopycnals. Under the reduced-gravity approximation, a buoyant region of light water with outcropping boundaries in the vicinity of the equator is described by two parameters: the meridional-to-zonal scale aspect ratio δ and the ratio γ of the Coriolis force to the pressure force on its meridional boundary. For realistic parameters (δ ～ 10~(-1); γ ～ 1), the lens, initially at rest, spreads eastward in accord with nonrotating gravity current dynamics, whereas its westward extrusion is arrested so that the western edge splits into two anticyclonic vortices. Meanwhile finite-amplitude westward-propagating inertial wave motions develop at the interface between the spreading current and the ambient fluid. The inertial wave structure is shown to be consistent with the structure of stable wave modes predicted by linear analysis of small amplitude perturbations superimposed on a zonally symmetric equatorial current with outcropping isopycnals. A Wentzel-Kramers-Brillouin-Jeffreys ray-tracing analysis indicates that the inertial wave is emitted during the early stage of the gravity current evolution and then dispersed on the spreading current.
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Nonlinear interactions of the barotropic Rossby waves propagating across the equator with trapped baroclinic Rossby or Yanai modes and mean zonal flow are studied within the two-layer model of the atmosphere, or the ocean. It is s...
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Nonlinear interactions of the barotropic Rossby waves propagating across the equator with trapped baroclinic Rossby or Yanai modes and mean zonal flow are studied within the two-layer model of the atmosphere, or the ocean. It is shown that the equatorial waveguide with a mean current acts as a resonator and responds to barotropic waves with certain wavenumbers by making the trapped baroclinic modes grow. At the same time the equatorial waveguide produces the barotropic response which, via nonlinear interaction with the mean equatorial current and with the trapped waves, leads to the saturation of the growing modes. The excited baroclinic waves can reach significant amplitudes depending on the magnitude of the mean current. In the absence of spatial modulation the nonlinear saturation of thus excited waves is described by forced Landau-type equation with one or two attracting equilibrium solutions. In the latter case the spatial modulation of the baroclinic waves is expected to lead to the formation of characteristic domain-wall defects. The evolution of the envelopes of the trapped Rossby waves is governed by driven Ginzburg-Landau equation, while the envelopes of the Yanai waves obey the "first-order" forced Ginzburg-Landau equation. The envelopes of short baroclinic Rossby waves obey the damped-driven nonlinear Schrodinger equation well studied in the literature.
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Resonant excitation of coastal Kelvin waves by free inertia-gravity waves impinging on the coast is studied in the framework of the simplest baroclinic model: two-layer rotating shallow water with an idealized straight coast. It i...
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Resonant excitation of coastal Kelvin waves by free inertia-gravity waves impinging on the coast is studied in the framework of the simplest baroclinic model: two-layer rotating shallow water with an idealized straight coast. It is shown that, with respect to the previous results obtained with the one-layer model, new resonances leading to a possible excitation of Kelvin waves appear. The most interesting ones, described in the paper, are resonances of a baroclinic inertia- gravity wave with either another wave of this kind, or with a coastal current, leading to generation of a barotropic Kelvin wave. A forced Hopf equation results in any case for the evolution of the Kelvin wave amplitude.
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Nonlinear interactions between the baroclinic Rossby waves trapped in the equatorial waveguide and the barotropic Rossby waves freely propagating across the equator are studied within the two-layer model of the atmosphere, or the ...
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Nonlinear interactions between the baroclinic Rossby waves trapped in the equatorial waveguide and the barotropic Rossby waves freely propagating across the equator are studied within the two-layer model of the atmosphere, or the ocean. It is shown that a barotropic wave can resonantly excite a pair of baroclinic waves with amplitudes much greater than its proper amplitude. The envelopes of the baroclinic waves obey Ginzburg-Landau-type equations and exhibit nonlinear saturation and formation of characteristic "domain-wall" and "dark-soliton" defects.
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Self-consistent finite-mode approximations for both Euler and Navier-Stokes equations for vorticity on a sphere are constructed and extended to the case of a rotating sphere, aiming at application to ocean and atmosphere modeling....
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Self-consistent finite-mode approximations for both Euler and Navier-Stokes equations for vorticity on a sphere are constructed and extended to the case of a rotating sphere, aiming at application to ocean and atmosphere modeling. In the absence of dissipation they preserve the specific Hamiltonian structure of hydrodynamics and have, at cach level of approximation, an appropriate number of integrals of motion, which is not the case for standard schemes.
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We study the adjustment of the tropical atmosphere to localized surface heating using a Lagrangian atmospheric model (LAM) that simulates a realistic Madden-Julian oscillation (MJO)-the dominant, eastward-propagating mode of tropi...
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We study the adjustment of the tropical atmosphere to localized surface heating using a Lagrangian atmospheric model (LAM) that simulates a realistic Madden-Julian oscillation (MJO)-the dominant, eastward-propagating mode of tropical intraseasonal variability modulating atmospheric convection. Idealized warm sea surface temperature (SST) anomalies of different aspect ratios and magnitudes are imposed in the equatorial Indian Ocean during MJO-neutral conditions and then maintained for 15 days. The experiments then continue for several more months. Throughout these experiments, we observe a robust generation of an MJO event, evident in precipitation, velocity, temperature, and moisture fields, which becomes a key element of atmospheric adjustment along with the expected Kelvin and Rossby waves. The MJO circulation pattern gradually builds up during the first week, and then starts to propagate eastward at a speed of 5-7 m s~(-1). The upper-level quadrupole circulation characteristic of the MJO becomes evident around day 14, with two anticyclonic gyres generated by the Gill-type response to convective heating and two cyclonic gyres forced by the excited Kelvin waves and extra-tropical Rossby wave trains. A moisture budget analysis shows that the eastward propagation of the MJO is controlled largely by the anomalous advection of moisture and by the residual between anomalous moisture accumulation due to converging winds and precipitation. The initial MJO event is followed by successive secondary events, maintaining the MJO for several more cycles. Thus, this study highlights the fundamental role that the MJO can play in the adjustment of the moist equatorial atmosphere to localized surface heating.
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Motivated by recent observations of coherent dipolar cyclone-anticyclone structures in the ocean, the modons, and their signature in the surface temperature field, we demonstrate that the classical modon solutions of the barotropi...
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Motivated by recent observations of coherent dipolar cyclone-anticyclone structures in the ocean, the modons, and their signature in the surface temperature field, we demonstrate that the classical modon solutions of the barotropic quasi-geostrophic equations can be generalized to include buoyancy or temperature as an active tracer. The properties of such "thermal" modons, and especially their ability to carry heat anomaly over long distances, depend on the relative sign of the associated vorticity and buoyancy anomalies. We show using numerical simulations with the thermal shallow water equations, and their quasi-geostrophic version, that the evolution of the modons is consistent with the observations.
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